1. Field of the Invention (Technical Field)
Embodiments of the present invention relate to eliminating the need for anti-aliasing filters in digital relays by use of oversampling.
2. Description of Related Art
Digital relays use sampling rates ranging from 8 samples/cycle to as high as 96 samples/cycle (in any case, less than 100 samples/cycle). During the inception of a fault, the voltage and current waveforms are superimposed by transients. The amount and duration of transients depend on factors like the instant of fault with respect to the voltage waveform, the type of fault, the location of fault on the line, and the damping available in the system. Faults occurring at instants when the voltage waveform is around its peak value are the most severe in terms of transients. Typically, voltage waveforms experience more severe transients than current waveforms. Digital relays use the discrete Fourier transform (DFT) of the sampled signal to estimate the phasor value of the fundamental. To avoid aliasing, especially during a fault, all digital relays employ an analog (low-pass) anti-aliasing filter before sampling the voltages and currents with a analog-to-digital converter (ADC). Such a filter introduces a time-delay of 1.5-2 ms in the phasor estimation depending on the sampling rate chosen. Such a filter can also be relatively expensive.
In many applications, oversampling, i.e., fs>>2fn where fs and fn are the sampling and Nyquist frequencies respectively has long been used to simplify the requirement of an anti-aliasing filter with a sharp cutoff at fn. If the oversampling rate is selected such that any aliased frequencies are extremely small or below the noise floor, then the anti-aliasing filter can be made less sharp or in some cases even be eliminated, reducing cost and delay. Many commonly-available ADCs utilize oversampling for these reasons.
Very inexpensive ADC chips are currently available that use oversampling up to a few hundred kHz. Digital music industry today is able to produce excellent sound re-production by using very simple or no analog pre-filtering in their products. Since adopting inexpensive oversampling can eliminate comparatively more expensive analog filter and the associated time-delay, it is worthwhile to investigate the possibility of removing anti-aliasing filters from digital relays through oversampling.
Power System Relaying Committee Report, “Software models for relays,” published in IEEE Trans. Power Delivery, vol. 16, no. 2, pp. 238-245, April 2001, indicates that oversampling is used in the newest generation of relays, but the main purpose of oversampling is oscillography. These relays still use an analog anti-aliasing filter and the sampling rate used for phasor estimation is obtained by decimating the data sampled at higher frequency.
There is thus value and a need for a method and apparatus which facilitates the manufacturing of a digital relay that does not require an analog anti-aliasing filter.